JPS6156976A - Transfer function measuring apparatus - Google Patents

Abstract

PURPOSE:To perform an analysis of transfer function accurately and effectively by a method wherein a stimulus signal given to a sample equipment and a response signal generated are multiplied by descrete complex exponential function to generate Fourier transforms of both the signals with the integration of the resulting multiplication signal. CONSTITUTION:A stimulus signal is applied to a sample equipment 7 from a stimulus signal source 11 to excite a response signal. A switching circuit 13 selects either stimulus signal or esponse signal and a sampler 15 performs a sampling of a signal one each clock cycle from a clock signal source 17. Signal sources 21 and 23 and mixers 25 and 27 are provided to multiply an output signal of the samler 15 by a descrete complex exponential function using a trigonometric identity. Then, low-pass filters 31 and 33 remove multiplication signal components above the frequency of the stimulus signal to get rid of several harmonics due to non-linearity and integrators 55 and 57 integrate the multiplication signal to obtain approximate figures in the Fourier transforms of the stimulus signal and the response signal. Then, a processor 59 divides the Fourier transform of the response signal by the Fourier transform of the stimulus signal to determine the transfer function of the sample equipment 7.

Description

[Detailed description of the invention]

[Field of Application in Industry-1-] The present invention relates to a transfer function measuring device for measuring the transfer function of an electrical or mechanical device under test. [Prior Art] In general, when a stimulus signal is applied to an electrical or mechanical device under test, a response signal of the device to this is measured, and the stimulus signal and the response signal are compared. The transfer function of the test device can be analyzed. and the real and imaginary parts of the Fourier transform of the stimulus signal, response signal are determined by multiplying these signals by a complex exponential function and then integrating over an integer number of cycles of the frequency associated with this signal. I can do it. An example of a conventional transfer function measurement device using analog technology is the two-channel swept frequency response analyzer (Model No. 916) manufactured by Bafco Co. This involves applying an analog stimulus signal to the device under test, and using the analog stimulus signal and response signal as part of the transfer function measurement.1. It is used to integrate. In conventional techniques using such analog calculation methods, the IF accuracy tends to be lower than in digital calculation methods. FIG. 6 is a block diagram showing a conventional transfer function measuring device using continuous signal and analog techniques. In Figure 6, both the stimulus and response signals are expressed by two functions according to the trigonometric identity: C05(ωt)
: So that it is equivalent to multiplication by −jsin(ωt) −
jωt is multiplied by a complex exponential function e. Integrating the generated signal over an integer number of cycles at the frequency in question provides an estimate of the real and imaginary parts of the Fourier transforms of the stimulus and response signals, and the contribution of higher harmonics at minutes are removed. Subsequent processing allows the transfer function of the device under test to be measured. Since only continuous signals are used, only small changes within the duration of the integration period have little or no effect on the measurement accuracy. However, when the change becomes large, measurement accuracy deteriorates. [Problems to be solved by the invention] This invention solves l.
This was done to eliminate the drawbacks listed below.
It uses digital technology to accurately and effectively analyze transfer functions. [Means for solving the problem] 31 According to an embodiment of the present invention, the first stimulation signal given to the device under test and the response signal generated thereby are sampled, and these two signals are is multiplied by a discrete complex exponential function, and the multiplied signal is integrated to produce a Fourier transform of the stimulus signal and response signal. The transfer function is then obtained by dividing the Fourier transform of the response signal by the Fourier transform of the stimulus signal. Note that the measurement of the integral of each multiplied signal is determined by summing the series of data points at the center,
This is done by adding thereto a preceding series of data points multiplied by a data independent leading weighting function and a subsequent series of data points multiplied by a data independent trailing weighting function. [Operation] This measuring device is capable of determining the transfer function of the device under test at any stimulus signal frequency within a predetermined range.・
Accuracy is independent of the period of the stimulation signal and the relationship between stimulation signal frequency and sampling rate. Therefore, the period of integration need not start or end at discrete data points. For example, if the period of integration ends between two adjacent discrete data points, the measuring device measures the integral between two adjacent discrete data points using the modified subsequent weighting polynomial. . Therefore, even if the frequency of the stimulation signal changes, the measurement accuracy does not change. [Embodiment of the Invention] Fig. 1 is a front view of a transfer function measuring device constructed according to an embodiment of the present invention. In FIG. 1, ] is the main body of the measuring device, which generates a stimulus signal such as a sinusoidal wave or a linearly or logarithmically swept sinusoidal curve. The measuring device body 1 can also be used to excite an electrical or mechanical device under test 7 with a stimulation signal and to record a response signal from the device under test 7. In addition, various parameters and commands can be sent via the front panel 5, and the results of transfer function measurement can be sent to the cathode ray tube (CRT).
) displayed above 3′. FIG. 2 is an electrical block diagram of the main body 1 of the measuring device 1 shown in FIG. In the figure ζε, 11 is a signal source which applies a stimulus signal such as a sine wave or a linearly or logarithmically stepped sine wave to the device under test 7, thereby exciting a response signal. Here, the stimulus signal and the response signal can each be processed in separate channels or sent to a switch circuit 13 as shown in FIG. This switch circuit 13 is used to select some signal and process it according to the first channel. Since both signals are processed in exactly the same way, for clarity this selected continuous signal will hereinafter be denoted as A(t). Next [! The clock source 171.1 sends an output signal at frequency fc to the zambler 15, which samples the signal A(t) once per clock cycle. Note that the output signal of the zambrar 15 is expressed as a discrete signal ^(n). The signal sources 21, 23 and mixers 25, 27 transform the signal ^(n) into a discrete complex exponential function e expressed as cos(ωn) -jsin(ωn) using the royal angle identity. (where ω is the normalized angular frequency defined as 2πrs/rc and Js is the frequency of the given stimulus signal in the analyzed power transfer function). Low pass filters 31,33 are used to remove this multiplied signal component below the stimulus signal frequency, thereby removing some harmonics due to non-linearities. Integrators 55 and 57 integrate the multiplied signals, thereby obtaining an approximation of the Fourier transform of the stimulus and response signals. The processor 59 divides the Fourier transform of the response signal by the Fourier transform of the stimulus signal in order to determine the transfer function of the device under test 7. The period of integration consists of an integer number of cycles of the stimulus signal frequency. For convenience of clarity, the output signal of the low-pass filter 31 will hereinafter be denoted as 5(n). Here, since integrators 57 and 55 operate in the same manner, integrator 55
I will explain its operation only. First, function generator 4
1.43 generates leading and trailing weighting polynomials, and multiplier 45 multiplies the leading part of the data points by the coefficients of the leading weighting polynomial and the trailing part of the data points by the coefficients of the trailing weighting polynomial. Adder 5I also adds the product of the preceding data point and the preceding weighting polynomial coefficient and the product of the succeeding data point and the succeeding weighting polynomial coefficient to the central portion of the data points. -7 = If the assumption is made that the device under test 7 is linear (this is necessary for the definition of the transfer function), then the clock frequency fc
can theoretically be as low as the Nyquist rate of twice the stimulus signal frequency S. In practice, the number of data points that can be used to measure individual integrals increases with increasing clock frequency C. Therefore, the sampling rate affects the accuracy with which the transfer function is measured.For a fifth-order fit (N-5), the clock frequency f
If c was about 10 times the stimulus signal frequency, a dynamic range of about 80 dB was obtained. FIG. 3 shows the case where the integration period T of signal 5(t) begins at exactly a discrete data point (n=0) and ends at exactly a discrete data point (n=12). In this case, the measurement of the integral using only the first-order fit yields (n= O) ~ (n-
12) only requires the addition of the data points. , otherwise, as shown in FIG. 2, the integral can also be viewed as: −8==In general, the integration period T is not an integral multiple of n. In this case, as shown in FIG. 4A, the period T begins at a discrete data point, but ends between two adjacent discrete data points. Of course, if we perform direct ti addition, an incorrect integration will be obtained, so we must use some method to calculate n
= 5(t) between IF and n-13 with period T
must be included in the overall integral of 5(t) at . In Figure 948, n=IL! , n=13 is defined as width W. Here 1
Normalize the m-order of d so that d=1, and d is n and (n
+ 1 ), the width W is between 0 and 1. p is defined as an integer number of discrete data points within period T, excluding the starting point at n=0. Degree N of weighted polynomial
defines the order of the polynomial fit to the measured data □. Of course, the smallest (t1) data point must be measured for the order Nth fit. The number of data points on either side of each individual integral section (eg, between n=5 and n=6) that is used to create an N-order fit for that integral section. If both sides are the same number and N is of odd order, then M-
(1-N)/2. The measuring device shown in FIG. 1 consists of (i) a central region of data points, (11) a leading region multiplied by the coefficient CL of a leading weighting polynomial;
Measure the integral over the entire period T by computing the sum of each subsequent region times the coefficient Et of the subsequent weighted polynomial. Since the preceding weighting polynomial only depends on the desired fit order, it can be derived immediately once N and M are known. However, the subsequent weighting polynomial depends on the fit order and also on the partial width W. Next, the period T can be set to start at n = 0, so the width W is defined by the frequency S and L, and as soon as the frequency S is known, it can be derived.
Ru. Those skilled in the art will appreciate that if N is an even number, then if a W number of data points are used on either side of the integral 71
: to 'j can extract the coefficients when the period T does not start at n=0. The measuring device shown in Figure 1 can be very roughly described as follows:
It can be viewed as measuring the integral over the entire period T by repeatedly measuring individual integral parts between adjacent discrete data points and then summing the individual integral values. The final integral 1M<minutes occupied by the subregion W of the distance between two adjacent discrete data points (for example between n-12 and n-13 in FIG. 4A) is added to the addition. The Nth order coefficient of the pre-weighted polynomial is multiplied by the 5(n) (N41) data points adjacent to the individual integral being measured. For example, in Figure 4A, n=
The integral of 5(L) between 0 and n=1 converts the (N Il ) preceding weighted polynomial coefficients to the data point S(n'---2)
Measured with N = 5 by multiplying by ~S (n = 3) and then adding the results. Note that the contribution of the subregion to the integral will be explained below. The coefficient CL of the preceding Nth order weighted polynomial is obtained from the following equation. Here, 13L is a coefficient of an intermediate N-dimensional weighted polynomial. Furthermore, provided that q=0.1,2. ......, N formula [4]
As a result, N continuous γ equations with N unknowns are obtained for the solution of coefficient 13L. In formula [3], y
is a fitting polynomial, the only N degree polynomial passing through all (Nll) data points. . The total period of integration T is divided into two parts such that T-p+W. Here, W is the final partial area of 5(t) (Fig. 4A..., 12 and □-+ mv lft1')
A width, yes, 91. When is normalized to +E, it is between 0 and 1. Using equation [3], the integral over period p is Oj''o j j2o t=. Here, YJ is the fitting polynomial over the third segment of 5(t) in period T. S′pS(・)d・−・・・・[6] 4 0 4 ・ By changing the order of addition, equation [6] can be written as follows: ゛S 5(n)dn−”・(7)'
L”0 + IllN-3(+P4N-1) Here, in order to simplify the formula, the preceding weighted polynomial coefficient CL is defined as follows: Cz-Σ nt (However, 0≦2≦N- 1) Cz-Σ
ntcttl, ≦2≦p−+) L[8]j”
0 and the coefficient t (the sum of 1 is equal to 1, so formula [7]
can be written in terms of the preceding polynomial coefficient Ct as follows. SS(n)dn-co-8(M)1C1・S(M]1)
→...Finally, the formula

[9] can be written as three addition formulas for cylinderization. Oj -(1 1)+N-1 10Σ CL-8(MIL) ...[10]t
-1) Formula [The sum of the second term on the right side of IO3 is 5(t
), where the sum of the coefficients BL is ■
, it is a Fll filter with a gain of ■:
, ” fl JTI jZ B b 'l--/
i iZi '11 m # -): iJ"f! 3
m (7) Tfl Ei corresponds to the edge outside the central region, and it is included in the sum and weighted to obtain the Nth order approximation of S([) at both ends of the period T. Note that if the integration period T begins and ends with M numerical data points and each M/2 point of the segment is used, then the coefficients of the sum of the first and third terms are the same and The order is reversed. To achieve integration over the entire integration period T, 2
It is also necessary to include the offset of the partial area W between two adjacent individual data points. Therefore, as shown in FIG.
> minutes must be included. Since the width of the measured partial integral segment is W instead of the width (d·1) used for the previous Nth weighted polynomial, the new coefficients of the Nth weighted polynomial of the subdomain Dj must be used. The coefficient DL can be derived as follows. Here, and since the region W lies between the adjacent discrete data points of number p1''1 and number (P41) l], thus, the total integral of 5(t) from 0 to T is S 5(n) dn= j=0 Therefore, it is actually better to characterize the integral as a separate addition of the data domain rather than as a repeated multiplication, addition operation. Accurate. It should also be noted that in the matrix representation: W = D (M) and D = Yl: M'l-'
...[15] In formula [15], W-[W, W*/2. W3/3. ...Bow ...Medium 6〕D= [DD, D,, D,, ...]
...]Mountain 7]-16 ~Here, since [M]' can be calculated in advance regardless of W, D can be determined by simply multiplying the vector by the matrix. Therefore, since we only need to repeat the minimum number of calculations 2 for each individual measurement,
Measurements can be made very quickly. Each addition formula of the last two terms in equation [14] can be combined with L to define the coefficient pt of the subsequent N-th degree weighted polynomial as follows: R'=C +D (only 17.1≦2≦N
)z Z+p-I Z-1R=D
(However, Z=N+1) ・・・・・・[19]
z N Using the subsequent polynomial coefficient skin, equation [14] can be written as a median such that the total integral over period T becomes: It should be noted that the period of L:1 integration does not necessarily have to start with discrete data. If a period starts between two adjacent discrete data points and ends between two adjacent data points, r, then the total integral (,1, defines another subregion at the beginning of the integration period, 1", 2 and 3, and a new weighting polynomial having the same form as the subsequent IRI +U multir(i, +E can be defined. FIG. 1 is a flowchart of each step performed on the measuring device main body 1 shown in FIG. 1. In steps 71 to 75,
The user determines the parameters of the transfer function and calculates the polynomial coefficients C
A new IEL is calculated. The coefficient cL is the above formula [4], [8
], and the coefficient rXt can be determined by the above C4,), [
8), can be determined using the formula [+21[+9]. Also, the coefficient CL
Since the measurements are independent, they can be measured once and then stored in a lookup table for future reference. Excitation and sampling are performed in steps 77 and 79. In step 91, the Fourier transform of either the stimulus signal or the response signal is measured. The decision is made and Zl, Zf, 3-117 are the same for both signals. Determination of the real or imaginary part of the selection signal is made in step 91 as a result of multiplication by IE sine or cosine functions. In steps 93 to 95, the sine function or cosine function is
A multiplication is performed, and the multiplied signal is filtered. Steps 97 to 117 are the Tosan signal that has been passed through the filter.
; Perform the integration of 5(n). In steps 97-103,
The sum of the preceding region data points times the coefficient Ct of the preceding weighting polynomial is added to the grand total. In steps 105-109, the central region data points are added to the grand total. In steps 111 to 117, the coefficient PL of the subsequent weighting polynomial
The data points of the double subsequent area are added to the grand total. In addition,
The order in which the three parts of the addition formula are added is not important. At this point the grand total is multiplied and passed through the filter by 1
．． The summation is thus the real or imaginary part of the Fourier transform of the stimulus or response signal.Finally, the transfer function is It can be obtained by dividing the Fourier transform of the time-domain response signal by the Fourier transform of the time-domain stimulus signal or by other well-known methods such as trispectral averaging. - The use of digital techniques provides a highly accurate transfer function measurement device. Also, the period of integration does not have to start or end at individual data points, so the frequency of the stimulus signal changes. However, the measurement accuracy does not change.

[Brief explanation of drawings]

FIG. 1 shows the configuration of a transfer function measuring device according to an embodiment of the present invention, an 11-plane view, FIG. 2 an electrical block diagram thereof, and FIG. it(
Waveform diagram showing exact start and end cycles, Figure 48 O, L
4B and 4B are waveform diagrams of the signal to be integrated over the beginning and end periods between two adjacent data points of the independent γ1- data point, and FIG. FIG. 6 shows a block 1'X1 of a transfer function measuring device from Tit using continuous wave, L and analog I wave technology. . In the figure, l is the measuring device body, and 3 is C'l? T, 5) 11
1 to panel, 7 is the device under test, 11 is the stimulation part source, 1
3 is a switch circuit, 15 is a sampler, 17 is a knock signal source, 21.23 is a signal source, 25.27 is a mixer, 3
2.33 is a low-pass filter, 41.43 is a function generator, 4
5.47 is a multiplier, 51.53 is an addition Z, 55.57 is an integrator, and 59 is a processor. Note that the same reference numerals in each figure indicate the same or corresponding parts.

Claims (1)

[Claims] A transfer function measuring device comprising the following (a) to (l). (b) Excitation means coupled to the device under test for applying a stimulation signal to the device under test; (b) Acquisition means for acquiring the signal; (c) Selecting either the stimulation signal or the response signal. (d) a sampler connected to the acquisition means for sampling and means for generating a plurality of sampling signals thereby; ) separating means connected to the sampler and for separating the sampling signal into three parts, leading, central and trailing; (f) leading generating means for generating coefficients of a leading weighting function; (g) trailing weighting function; (h) preceding multiplier means coupled to said separation means and preceding generating means for multiplying the sampling signal of the preceding portion by the coefficients of the preceding weighting function; ) subsequent multiplier means coupled to said separation means and subsequent generation means for multiplying the sampled signal of the subsequent portion by a coefficient of a subsequent weighting function; Addition means coupled to each preceding and subsequent multiplication means and separation means for summing the sampling signals; (l) calculation means coupled to said addition means for computing a transfer function;